It is well known that mobile terminal operation can be degraded by the presence of a strong interfering signal. For example, a nearby mobile terminal or base station operating at a different frequency can produce strong interfering signals. Furthermore, communications industries, and in particular, the cellular communication industry desires an ability to transmit and receive signals in two separate bands at the same time within a single mobile terminal. However, implementing such a request practically guarantees strong signal interference within the single mobile terminal.
In the short term, a desire to talk and surf the web simultaneously on a single band is not possible due to shortcomings in the Evolution-Data Optimized (EVDO) standard. As a result of these shortcomings, a requirement has emerged for mobile terminals that can operate simultaneously on code division multiple access (CDMA) Band 5 for voice and long term evolution (LTE) Band 13 for data. This requirement is known as simultaneous voice/LTE (SV-LTE).
Unfortunately, due to the aforementioned interference problems, SV-LTE cannot be facilitated by simply operating two cellular front ends at the same time. The major reason that a strong interferer signal degrades mobile terminal operation is a generation of third-order intermodulation (IM3) products in nonlinear electronic components such as RF switches that the signals encounter. This nonlinear phenomenon is a result of compression and/or clipping of the high-power signals as their levels exceed the linear dynamic range of the electronic components. If a signal A is incident upon an electronic component that compresses the signal A, a resulting signal Acompressed can be modeled with an odd-order power series as follows in expression (1):A→Acompressed=α0A−α1A3+α2A5−α3A7+ . . .  (1)
If the compression is relatively light, the coefficients α2, α3, and higher are negligibly small, and the power series can be truncated after the cubic term α1A3. Therefore, the signal Acompressed is approximated by expression (2).Acompressed≈α0A−α1A3.  (2)
Now consider the signal A and another signal B that simultaneously engage an electronic component. If the electronic component is perfectly linear, a resultant signal is a superposition of the signal A and the signal B (i.e., A+B). However, practical electronic components suffer from various degrees of nonlinearity. Therefore, a cubic third-order term α1(A+B)3 is included in expression (3) to more accurately model the resultant signal (A+B)compressed.(A+B)→(A+B)compressed≈α0(A+B)−α1(A+B)3.  (3)
Expanding the (A+B) of the cubic third order term α1(A+B)3 into a full polynomial yields the expression (4).(A+B)3=A3+3A2B+3AB2+B3  (4)
If the signal A and the signal B are both sinusoidal the following expressions (5a) and (5b) are given.A=a·sin(ω1t+φ1)  (5a)B=b·sin(ω2t+φ2),  (5b)
The following trigonometric identities represented by expressions (6), (7), and (8) can be applied to expression (4).sin3 x=¼(3 sin x+sin 3x)  (6)sin2 x=½(1−cos 2x)  (7)sin x cos y=½[sin(x+y)+sin(x−y)].  (8)
Expanding out the third-order polynomial from expression (4) using the sinusoidal signals of expressions (5a) and (5b), it can be seen that the cubic third order term α1(A+B)3 results in additional frequency content as shown below in expression (9).
                                          [                                          a                ·                                  sin                  ⁡                                      (                                                                  ω                        1                                            +                                              ϕ                        1                                                              )                                                              +                              b                ·                                  sin                  ⁡                                      (                                                                  ω                        2                                            +                                              ϕ                        2                                                              )                                                                        ]                    3                =                                            (                                                3                  ⁢                                      /                                    ⁢                  4                  ⁢                                                                          ⁢                                      a                    3                                                  +                                  3                  ⁢                                      /                                    ⁢                  2                  ⁢                                                                          ⁢                                      ab                    2                                                              )                        ·                          sin              ⁡                              (                                                                            ω                      1                                        ⁢                    t                                    +                                      ϕ                    1                                                  )                                              +                                    (                                                3                  ⁢                                      /                                    ⁢                  4                  ⁢                                                                          ⁢                                      b                    3                                                  +                                  3                  ⁢                                      /                                    ⁢                  2                  ⁢                                                                          ⁢                                      a                    2                                    ⁢                  b                                            )                        ·                          sin              ⁡                              (                                                                            ω                      2                                        ⁢                    t                                    +                                      ϕ                    2                                                  )                                              -                      1            ⁢                          /                        ⁢            4            ⁢                                                  ⁢                          a              3                        ⁢                          sin              ⁡                              (                                                      3                    ⁢                                          ω                      1                                        ⁢                    t                                    +                                      3                    ⁢                                          ϕ                      1                                                                      )                                              -                      1            ⁢                          /                        ⁢            4            ⁢                          b              3                        ⁢                          sin              ⁡                              (                                                      3                    ⁢                                          ω                      2                                        ⁢                    t                                    +                                      3                    ⁢                                          ϕ                      2                                                                      )                                              -                      3            ⁢                          /                        ⁢            2            ⁢                          a              2                        ⁢            b            ⁢                                                  ⁢                          sin              ⁡                              (                                                                            [                                                                        2                          ⁢                                                      ω                            1                                                                          +                                                  ω                          2                                                                    ]                                        ⁢                    t                                    +                                      2                    ⁢                                          ϕ                      1                                                        +                                      ϕ                    2                                                  )                                              -                      3            ⁢                          /                        ⁢            2            ⁢                          ab              2                        ⁢                          sin              ⁡                              (                                                                            [                                                                        ω                          1                                                +                                                  2                          ⁢                                                      ω                            2                                                                                              ]                                        ⁢                    t                                    +                                      ϕ                    1                                    +                                      2                    ⁢                                          ϕ                      2                                                                      )                                              +                      3            ⁢                          /                        ⁢            2            ⁢                          a              2                        ⁢            b            ⁢                                                  ⁢                          sin              ⁡                              (                                                                            [                                                                        2                          ⁢                                                      ω                            1                                                                          -                                                  ω                          2                                                                    ]                                        ⁢                    t                                    +                                      2                    ⁢                                          ϕ                      1                                                        -                                      ϕ                    2                                                  )                                              +                      3            ⁢                          /                        ⁢            2            ⁢                                                  ⁢                          ab              2                        ⁢                                          sin                ⁡                                  (                                                                                    [                                                                              -                                                          ω                              1                                                                                +                                                      2                            ⁢                                                          ω                              2                                                                                                      ]                                            ⁢                      t                                        -                                          ϕ                      1                                        +                                          2                      ⁢                                              ϕ                        2                                                                              )                                            .                                                          (        9        )            
In addition to the original frequencies, ω1 and ω2, the expression (9) demonstrates that compression results in new products at the third harmonic frequencies, 3ω1 and 3ω2, as well as four additional intermodulation frequencies, 2ω1±ω2 and 2ω2±ω1. These last four are third order intermodulation (IM3) products, and two in particular, 2ω1−ω2 and 2ω2−ω1, tend to be problematic because they are relatively close in frequency to the original signals. As a result, the 2ω1−ω2 and 2ω2−ω1 IM3 products cannot be easily attenuated with a simple low-pass filter. Hereinafter, following the assumption that ω2>ω1, the IM3 product 2ω1−ω2 is designated as IM3down and the IM3 product 2ω2−ω1 is designated as IM3up to represent the IM3 products just below and just above the transmit frequencies, respectively. Furthermore, subsequent references herein to “IM3 products” will refer only to IM3up and IM3down, as the two additional IM3 products at 2ω1+ω2 and 2ω2+ω1 are not a particular concern of this disclosure.
FIG. 1 is a frequency spectrum for universal mobile telecommunications system (UMTS) band 5 (B5) and evolved UMTS terrestrial radio access (E-UTRA) band 13 (B13). The frequency spectrum of FIG. 1 illustrates the impact of the IM3up and IM3down products generated by the simultaneous transmission of the signals A and B. Nonlinearity of electronic components is especially problematic in the case of SV-LTE because certain transmit channel combinations result in IM3 products that fall directly within the pass bands of the receivers. Therefore, unless such IM3 products can be dramatically reduced, receivers impacted by the IM3 products can be severely de-sensed and a mobile terminal that incorporates the impacted receivers will become essentially useless as long as the IM3 products are present.
FIG. 2 is a diagram illustrating a related art approach for reducing power in the IM3 products generated by a first nonlinear switch 10 and a second nonlinear switch 12. A first antenna 14 is used for transmission and reception of signals in a first band (B5) and a second antenna 16 is used for transmission and reception of a second band (B13). Since the first antenna 14 and the second antenna 16 can be designed to provide ˜10 dB of isolation, the resulting IM3 products can be reduced proportionally. However, even a 10 dB reduction in IM3 products requires a linearity that is on the order of 10-20 dB higher than current state-of-the-art electronic components such as the first nonlinear switch 10 and the second nonlinear switch 12. As such, there remains a need for additional intermodulation (IM) suppression to further reduce IM3 products and other IM products generated by RF systems having nonlinear elements that include nonlinear components that can be, but are not limited to filters, duplexers, RF switches, and combinations thereof.